The development of data processing systems, computers and computer applications has transformed different processes into computerized processes. One example of such a process is modeling. Modeling means that a model is created from a product under design for describing the product to be constructed, the model containing at least information needed to illustrate the product. A product may be composed of one or more articles. Computer applications typically apply predefined object types that are provided with values in connection with the modeling to create objects (models) of articles that exist or will exist (or at least are planned to exist) in the real world. Examples of these object types in the field of building modeling include beams, columns, plates and slabs. A product model may in principle comprise an unlimited number of objects.
Typically a product comprises real world articles that may be in touch with each other or have no contact. Real world articles may not overlap with each other. A corresponding model may comprise for a real world article one or more objects that may overlap with each other or be in touch with each other as well as have no contact. Especially, if an article has a complicated shape, it is common to model the article by using basic object types. Examples of such basic object types include a cube, a rectangle, a ball and a parallelogram. Even not so complicated shapes are easier to model by using basic object types that overlap as is obvious from FIG. 2A illustrating a single article (structure) and FIG. 2B showing basic objects used for forming the single article.
For illustrating the article or calculating filling volumes, like the amount of concrete needed to obtain a corresponding cast-in-situ structure (article), the basic objects are merged. One possibility to merge the objects is to use Boolean operations (union, intersection and difference), for example as described in “Boolean operations on multi-region solids for mesh generation” by André Maués Brabo Pereira, Marcos Chataignier de Arruda, Antônio Carlos de O. Miranda, William Wagner M. Lira, Luiz Fernando Martha, Engineering with Computers, July 2012, Volume 28, Issue 3, pp 225-239, DOI 10.1007/s00366-011-0228-8. The result of the merging by using Boolean operations is a single object formed by a real union of the merged objects. However, especially for complex models, forming the required real union is a rather complicated mechanism that uses quite a lot of computing capacity.